1. Field of the Invention
The present invention relates to a device having quantum-wave interference layers that reflect carriers, or electrons and holes, effectively. In particular, the invention relates to light-emitting semiconductor devices including a laser (LD) and a light-emitting diode (LED) with improved luminous efficiency by effectively confining carriers within an active layer. Further, the present invention relates to semiconductor devices including a field effect transistor (FET) and a solar cell with improved carrier reflectivity.
2. Description of the Related Art
An LD has been known to have a double hetero junction structure whose active layer is formed between n-type and p-type cladding layers. The cladding layers function as potential barriers for effectively confining carriers, or electrons and holes, within the active layer.
However, a problem persists in luminous efficiency. Carriers overflow the potential barriers of the cladding layers, which lowers luminous efficiency. Therefore, further improvement has been required, as presently appreciated by the present inventors.
As a countermeasure, forming cladding layers with a multi-quantum well structure of a first and a second layers as a unit has been suggested by Takagi et al. (Japanese Journal of Applied Physics. Vol. 29, No. 11, November 1990, pp. L1977-L1980). This reference, however, does not teach or suggest values of kinetic energy of carriers to be considered and the degree of luminous intensity improvement is inadequate.
The inventors of the present invention conducted a series of experiments and found that the suggested thicknesses of the first and the second layers by Takagi et al. were too small to confine electrons, and that preferable thicknesses of the first and second layers are 4 to 6 times larger than those suggested by Takagi et al. Further, the present inventors thought that multiple quantum-wave reflection of carriers might occur by a multi-layer structure with different band width, like multiple light reflection by a dielectric multi-film structure. And the inventors thought that it would be possible to confine carriers by the reflection of the quantum-wave. As a result, the inventors invented a preferable quantum-wave interference layer and applications of the same.
It is, therefore, a first object of the present invention to provide a quantum-wave interference layer, with high reflectivity to carriers, functioning as a reflecting layer. It is a second object of the present invention to improve quantum-wave reflectivity by additionally providing a new layer structure with a multi-layer structure whose band width is different with respect to each other. It is a third object of the invention to provide variations of a quantum-wave interference layer for effectively reflecting quantum-waves.
In light of these objects a first aspect of the present invention is a semiconductor device constituted by a quantum-wave interference layer having plural periods of a pair of a first layer and a second layer, the second layer having a wider band gap than the first layer. Each thickness of the first and the second layers is determined by multiplying by an odd number one fourth of a quantum-wave wavelength of carriers in each of the first and the second layers existing around the lowest energy level of the second layer.
The second aspect of the present invention is a semiconductor device constituted by a quantum-wave interference layer having plural periods of a first layer and a second layer as a unit. The second layer has a wider band gap than the first layer. A xcex4 layer is included for sharply varying an energy band and is formed between the first and the second layers. Each thickness of the first and the second layers is determined by multiplying by odd number one fourth of quantum-wave wavelength of carriers in each of the first and the second layers, and a thickness of the xcex4 layer is substantially thinner than that of the first and the second layers.
The third aspect of the present invention is to define each thickness of the first and the second layers as follows:
DW=nWxcexW/4=nWh/4[2mW(E+V)]1/2xe2x80x83xe2x80x83(1)
and
DB=nBxcexB/4=nBh/4(2mBE)1/2xe2x80x83xe2x80x83(2)
In Eqs. 1 and 2, h, mW, mB, E, V, and nW, nB represent a plank constant, effective mass of carrier in the first layer, effective mass of carrier in the second layer, kinetic energy of carriers at the lowest energy level around the second layer, potential energy of the second layer to the first layer, and odd numbers, respectively.
The fourth aspect of the present invention is a semiconductor device having a plurality of partial quantum-wave interference layers Ik with arbitrary periods Tk including a first layer having a thickness of DWk and a second layer having a thickness of DBk and arranged in series. The thicknesses of the first and the second layers satisfy the formulas:
DWk=nWkxcexWk/4=nWkh/4[2mWk(Ek+V)]1/2xe2x80x83xe2x80x83(3)
and
DBk=nBkxcexBk/4=nBkh/4(2mBkEk)1/2xe2x80x83xe2x80x83(4).
In Eqs. 3 and 4, Ek, mWk, mBk, and nWk and nBk represent plural kinetic energy levels of carriers flowing into the second layer, effective mass of carriers with kinetic energy Ek+V in the first layer, effective mass of carriers with kinetic energy Ek in the second layer, and arbitrary odd numbers, respectively.
The plurality of the partial quantum-wave interference layers Ik are arranged in series from I1 to Ij, where j is a maximum number of k required to form a quantum-wave interference layer as a whole.
The fifth aspect of the present invention is a semiconductor device having a quantum-wave interference layer with a plurality of partial quantum-wave interference layers arranged in series with arbitrary periods. Each of the plurality of partial quantum-wave interference layers is constructed with serial pairs of the first and second layers. The widths of the first and second layers of the serial pairs are represented by (DW1, DB1), . . . , (DWk, DBk), . . . , (DWj, DBj). (DWk, DBk) is a pair of widths of the first and second layers and is defined as Eqs 3 and 4, respectively.
The sixth aspect of the present invention is to form a xcex4 layer between a first layer and a second layer, which sharply varies the energy band and has a thickness substantially thinner than that of the first and second layers.
The seventh aspect of the present invention is a semiconductor device having a quantum-wave interference layer constituted by a plurality of semiconductor layers made of a hetero-material with different band gaps. The interference layer is constituted by a plurality of xcex4 layers for sharply varying the energy band and being formed at an interval of one forth of a quantum-wave wavelength of carriers multiplied by an odd number. The thickness of the xcex4 layers is significantly thinner than the width of the interval.
When a single level E of kinetic energy is adopted, the interval DB between the xcex4 layers is calculated by Eq. 2. When plural levels Ek of kinetic energy are adopted, the interval DBk between the xcex4 layers are calculated by Eq. 4. In the latter case, several partial quantum-wave interference layers Ik with the xcex4 layers formed at an interval DBk in Tk periods may be arranged in series from I1 to Ij to form a quantum-wave interference layer as a whole. Alternatively, the partial quantum-wave interference layer may be formed by serial S layers with intervals of DB1, . . . , DBk, . . . , to DBj, and the plurality of the partial quantum-wave interference layers may be arranged in series with an arbitrary period.
The eighth aspect of the present invention is to use the quantum-wave interference layer as a reflecting layer for reflecting carriers.
The ninth aspect of the present invention is to constitute a quantum-wave incident facet in the quantum-wave interference layer by a second layer with enough thickness for preventing conduction of carriers by a tunneling effect.
The tenth aspect of the present invention is a light-emitting semiconductor device constituted by an n-type layer, a p-type layer, and an active layer that is formed between the n-type layer and the p-type layer, and wherein one of the n-type layer and the p-type layer is the quantum-wave interference layer described in one of the first to ninth aspects of the present invention.
The eleventh aspect of the present invention is a light-emitting semiconductor device with a hetero-junction structure whose active layer is formed between an n-type conduction layer and a p-type conduction layer and one of the n-type and p-type conduction layers is the quantum-wave interference layer described in one of the first to tenth aspects of the present invention. The n-type and p-type conduction layers respectively function as an n-type cladding layer and a p-type cladding layer and carriers are confined into the active layer by being reflected by the quantum-wave interference layer.
The twelfth aspect of the present invention is a field effect transistor including the quantum-wave interference layer, described in one of the first to ninth aspects of the present invention, positioned adjacent to a channel.
The thirteenth aspect of the present invention is a photovoltaic device having a pn junction structure including an n-layer and a p-layer. At least one of the n-layer and p-layer is made of a quantum-wave interference layer described in one of the first to ninth aspects of the present invention for reflecting minor carriers as a reflecting layer.
(First and Third Aspects of the Invention)
The principle of the quantum-wave interference layer of the present invention is explained hereinafter. FIG. 1 shows a conduction band of a multi-layer structure with plural periods of a first layer W and a second layer B as a unit. A band gap of the second layer B is wider than that of the first layer W. Electrons conduct from left to right as shown by an arrow in FIG. 1. Among the electrons, those that exist around the bottom of the second layer B are likely to contribute to conduction. The electrons around the bottom of the second layer B has a kinetic energy E. Accordingly, the electrons in the first layer W have a kinetic energy E+V which is accelerated by potential energy V due to the band gap between the first layer W and the second layer B. In other words, electrons that move from the first layer W to the second layer B are decelerated by potential energy V and return to the original kinetic energy E in the second layer B. As explained above, kinetic energy of electrons in the conduction band is modulated by potential energy due to the multi-layer structure.
When thicknesses of the first layer W and the second layer B are equal to order of quantum-wave wavelength, electrons tend to have characteristics of a wave. The wave length of the electron quantum-wave is calculated by Eqs. 1 and 2 using kinetic energy of the electron. Further, defining the respective wave number vector of first layer W and second layer B as KW and KB, reflectivity R of the wave is calculated by:                                                         R              =                              xe2x80x83                            ⁢                                                (                                                            "LeftBracketingBar"                                              K                        W                                            "RightBracketingBar"                                        -                                          "LeftBracketingBar"                                              K                        B                                            "RightBracketingBar"                                                        )                                /                                  (                                                            "LeftBracketingBar"                                              K                        W                                            "RightBracketingBar"                                        +                                          "LeftBracketingBar"                                              K                        B                                            "RightBracketingBar"                                                        )                                                                                                        =                              xe2x80x83                            ⁢                                                (                                                                                    [                                                                              m                            W                                                    ⁡                                                      (                                                          E                              +                              V                                                        )                                                                          ]                                                                    1                        /                        2                                                              -                                                                  [                                                                              m                            B                                                    ⁢                          E                                                ]                                                                    1                        /                        2                                                                              )                                /                                  (                                                                                    [                                                                              m                            W                                                    ⁡                                                      (                                                          E                              +                              V                                                        )                                                                          ]                                                                    1                        /                        2                                                              +                                                                  [                                                                              m                            B                                                    ⁢                          E                                                ]                                                                    1                        /                        2                                                                              )                                                                                                        =                              xe2x80x83                            ⁢                                                [                                      1                    -                                                                  (                                                                              m                            B                                                    ⁢                                                      E                            /                                                                                          m                                W                                                            ⁡                                                              (                                                                  E                                  +                                  V                                                                )                                                                                                                                    )                                                                    1                        /                        2                                                                              ]                                /                                                      [                                          1                      +                                                                        (                                                                                    m                              B                                                        ⁢                                                          E                              /                                                                                                m                                  W                                                                ⁡                                                                  (                                                                      E                                    +                                    V                                                                    )                                                                                                                                              )                                                                          1                          /                          2                                                                                      ]                                    .                                                                                        (        5        )            
Further, when mB=mW, the reflectivity R is calculated by:
xe2x80x83R=[1xe2x80x98xe2x88x92(E/(E+V))1/2]/[1+(E/(E+V))1/2]xe2x80x83xe2x80x83(6).
When E/(E+V)=x, Eq. 6 is transformed into:
R=(1xe2x88x92x1/2)/(1+x1/2)xe2x80x83xe2x80x83(7).
The characteristic of the reflectivity R with respect to energy ratio x obtained by Eq. 7 is shown in FIG. 2.
When the second layer B and the first layer W have S periods, the reflectivity RS on the incident facet of a quantum-wave is calculated by:
RS=[(1xe2x88x92xS)/(1+xs)]2xe2x80x83xe2x80x83(8).
When the formula xxe2x89xa61/10 is satisfied, Rxe2x89xa70.52. Accordingly, the relation between E and V is satisfied with:
Exe2x89xa6V/9xe2x80x83xe2x80x83(9).
Since the kinetic energy E of conducting electrons in the second layer B exists around the bottom of the conduction band, the relation of Eq. 9 is satisfied and the reflectivity R at the interface between the second layer B and the first layer W becomes 52% or more. Consequently, the multi-layer structure having two kinds of layers with different band gaps to each other enables effective quantum-wave reflection.
Further, utilizing the energy ratio x enables the thickness ratio DB/DW of the second layer B to the first layer W to be obtained by:
DB/DW=[mW/(mBx)]1/2xe2x80x83xe2x80x83(10).
Thicknesses of the first layer W and the second layer B are determined for selectively reflecting one of holes and electrons, because of a difference in potential energy between the valence and the conduction bands, and a difference in effective mass of holes and electrons in the first layer W and the second layer B. Namely, the optimum thickness for reflecting electrons is not optimum for reflecting holes. Eqs. 5-10 refer to a structure of the quantum-wave interference layer for reflecting electrons selectively. The thickness for selectively reflecting electrons is designed based on a difference in potential energy of the conduction band and effective mass of electrons. Further, the thickness for selectively reflecting holes is designed based on a difference in potential energy of the valence band and effective mass of holes, realizing another type of quantum-wave interference layer for reflecting only holes and allowing electrons to pass through.
(Fourth Aspect of the Invention)
As shown in FIG. 3, a plurality of partial quantum-wave interference layers Ik may be formed corresponding to each of a plurality of kinetic energy levels Ek. Each of the partial quantum-wave interference layers Ik has Tk periods of a first layer W and a second layer B as a unit whose respective thicknesses (DWk, DBk) are determined by Eqs. 3 and 4. The plurality of the partial quantum-wave interference layer Ik is arranged in series with respect to the number k of kinetic energy levels Ek. That is, the quantum-wave interference layer is formed by a serial connection of I1, I2, . . . , and Ij. As shown in FIG. 3, electrons with each of the kinetic energy levels Ek are reflected by the corresponding partial quantum-wave interference layers Ik. Accordingly, electrons belonging to each of the kinetic energy levels from E1 to Ej are reflected effectively. By designing the intervals between the kinetic energies to be short, thicknesses of the first layer W and the second layer B (DWk, DBk) in each of the partial quantum-wave interference layers Ik vary continuously with respect to the value k.
(Fifth Aspect of the Invention)
As shown in FIG. 4, a plurality of partial quantum-wave interference layers may be formed with an arbitrary period. Each of the partial quantum-wave interference layers, I1, I2, . . . is made of serial pairs of the first layer W and the second layer B with widths (DWk, DBk) determined by Eqs 3 and 4. That is, the partial quantum-wave interference layer, e.g., I1, is constructed with serial layers of width (DW1, DB1), (DW2, DB2), . . . , (DWj, DBj), as shown. A plurality I1, I2, . . . of layers such as layer I1 are connected in series to form the total quantum-wave interference layer. Accordingly, electrons of the plurality of kinetic energy levels Ek are reflected by each pair of layers in each partial quantum-wave interference layers. By designing the intervals between kinetic energies to be short, thicknesses of the pair of the first layer W and the second layer B (DWk, DBk) in a certain partial quantum-wave interference layer varies continuously with respect to the value k.
(Second and Sixth Aspects of the Invention)
The second and sixth aspects of the present invention are directed to forming a xcex4 layer at the interface between the first layer W and the second layer B. The xcex4 layer has a relatively thinner thickness than both of the first layer W and the second layer B and sharply varies an energy band. Reflectivity R of the interface is determined by Eq. 7. By forming the xcex4 layer, the potential energy V of an energy band becomes larger and the value x of Eq. 7 becomes smaller. Accordingly, the reflectivity R becomes larger.
Variations are shown in FIGS. 8A to 8C. The xcex4 layer may be formed on both ends he every first layer W as shown in FIGS. 8A to 8C. In FIG. 8A, the xcex4 layers are formed so that an energy level higher than that of the second layer B may be formed. In FIG. 8B, the xcex4 layers are formed so that an energy level lower than that of the first layer W may be formed. In FIG. 8C, the xcex4 layers are formed so that the energy level higher than that of the second layer B and the energy level lower than that of the first layer W may be formed. As an alternative to each of the variations shown in FIGS. 8A to 8C, the xcex4 layer can be formed on one end of the every first layer W.
Forming one xcex4 layer realizes large quantum-wave reflectivity at the interface between the first layer W and the second layer B and a plurality of the xcex4 layers realizes a larger reflectivity as a whole.
(Seventh Aspect of the Invention)
The seventh aspect of the present invention is to form a plurality of xcex4 layers in second layer B at an interval DB determined by Eq. 2. Variations are shown in FIGS. 5 to 7. In FIG. 5, the xcex4 layer is formed so that an energy level higher than that of the second layer B may be formed. In FIG. 6, the xcex4 layer is formed so that an energy level lower than that of the second layer B may be formed. In FIG. 7, the xcex4 is formed alternately so that the higher and lower energy levels than the second layer B may be formed.
When a plurality of energy levels of electrons are set, the interval DB between the xcex4 layers in the second layer B corresponds to thicknesses DBk of the second layer B in FIGS. 3 and 4. Accordingly, a quantum-wave interference layer can be made from a serial connection of a number j of partial quantum-wave interference layers Ik as shown in FIG. 3. In this case, xcex4 layers are disposed at an interval DBk with period Tk in each partial interference layers and the number j corresponds to the kinetic energy of electrons. Alternatively, the xcex4 layers may be arranged at an interval from DB1 to DBj in series and may be formed in the second layer B so as to make the partial quantum-wave interference layers and the plurality of the partial quantum-wave interference layers, arranged in series as shown in FIG. 4.
(Eighth Aspect of the Invention)
The eighth aspect of the present invention is directed to a quantum-wave interference layer that functions as a reflecting layer and selectively confines carriers in an adjacent layer. As mentioned above, the quantum-wave interference layer can be designed to confine either electrons or holes selectively.
(Ninth Aspect of the Invention)
The ninth aspect of the present invention, or forming a thick second layer B0 at the side of an incident plane of the quantum-wave interference layer, and effectively prevents conduction by tunneling effects and reflects carriers.
(Tenth and Eleventh Aspects of the Invention)
According to the tenth and eleventh aspects of the present invention, the quantum-wave interference layer is formed in at least one of the p-type layer and an n-type layer sandwiching an active layer of a light-emitting semiconductor device and effectively realizes confinement of carriers in the active layer and increases output power.
(Twelfth Aspect of the Invention)
According to the twelfth aspect of the present invention, a quantum-wave interference layer is formed adjacent to a channel of a field effect transistor realizes effective confinement of carriers therein which conduct through the channel so as to improve an amplification factor of the transistor and signal-to-noise (S/N) ratio.
(Thirteenth Aspect of the Invention)
According to the thirteenth aspect of the present invention, a quantum-wave interference layer is formed in a photovoltaic device with a pn junction structure and reflects minor carriers to the p-type or n-type layer and prevents drift of the carriers to a reverse direction around the junction, improving opto-electric conversion efficiency.